Guys, I think I’ve cracked it!
Get hold of one end, look at the point where it enters the tangled mess and at the same time give it a gentle tug. Use a needle to pull it out through a couple of layers of yarn or so at a time.
Repeat a thousand times until done. Make sure that you keep yarn untangled at the other end. Work on a big sofa or bed without any distructions such as husbands, pets, and kids around.